Question

Determine whether the sequence converges, and if so find its limit.

Answer 1

\[\left\{( 1-\frac{ 2 }{ n } )^{n}\right\} \] n = 1, to infinity.

Answer 2

A sequence convergences if

\[ \lim_{n \rightarrow \infty} a_n = L \]

Where L is finite. Recall the limit definition of e

\[ e^a = \lim_{x \rightarrow \infty} (1 + \frac{a}{x})^x\]

That should help you obtain the limit of your sequence to see if it converges to a finite number.

Answer 3

Would it be: \[e^{-2}\]

Answer 4

Correct

Answer 5

Ok great. Thanks so much. I wasnt familiar with that rule!